The deformed figures of the Dedekind ellipsoids in the post-Newtonian approximation to general relativity - corrections and amplifications

Abstract

Two errors in the analysis of an earlier paper on the same subject are corrected. It is found that as a consequence of the corrections, the solution to the post-Newtonian equations (appropriate to determining the deformed figures of the Dedekind ellipsoid) now diverges at a point where the axes of the ellipsoid are in the ratios 1:0.3370:0.2850. In addition, the fourth-harmonic oscillations of the Dedekind ellipsoid are considered. It is found that it becomes dynamically unstable when its axes are in the ratios 1:0.3121:0.2680.